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Abstract: In this paper, we try to solve the semidefinite program with box constraints. Since the traditional projection method for constrained optimization with box constraints is not suitable to the semidefinite constraints, we present a new algorithm based on the feasible direction method. In the paper, we discuss two cases: the objective function in semidefinite programming is linear and nonlinear, respectively. We establish the convergence of our algorithm, and report the numerical experiments which show the effectiveness of the algorithm. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a new penalty-free-type method for nonlinear equality constrained problems. The new algorithm uses trust region framework and feasibility safeguarding technique. Moreover, it has no choice of penalty parameter and penalty function as a merit function, and it does not use the filter technique to avoid the penalty function either. We analyze the global convergence of the main algorithm under the standard assumptions. The preliminary numerical tests are reported. [Copyright &y& Elsevier]

Abstract: In this paper, a new feasible primal–dual interior point algorithm for solving inequality constrained optimization problems is presented. At each iteration, the algorithm solves only two or three reduced systems of linear equations with the same coefficient matrix. The searching direction is feasible and the object function is monotone decreasing. The proposed algorithm is proved to possess global and superlinear convergence under mild conditions. Finally, some numerical experiments with the algorithm are reported. [Copyright &y& Elsevier]